# PHYS 2212 Module 3

3: Electric Potential

The energy released in a lightning strike is an excellent illustration of the vast quantities of energy that may be stored and released by an electric potential difference. In this chapter, we calculate just how much energy can be released in a lightning strike and how this varies with the height of the clouds from the ground. (credit: modification of work by Anthony Quintano)

In Electric Charges and Fields, we just scratched the surface (or at least rubbed it) of electrical phenomena. Two terms commonly used to describe electricity are its energy and voltage, which we show in this chapter is directly related to the potential energy in a system.

We know, for example, that great amounts of electrical energy can be stored in batteries, are transmitted cross-country via currents through power lines, and may jump from clouds to explode the sap of trees. In a similar manner, at the molecular level, ions cross cell membranes and transfer information.

We also know about voltages associated with electricity. Batteries are typically a few volts, the outlets in your home frequently produce 120 volts, and power lines can be as high as hundreds of thousands of volts. But energy and voltage are not the same thing. A motorcycle battery, for example, is small and would not be very successful in replacing a much larger car battery, yet each has the same voltage. In this chapter, we examine the relationship between voltage and electrical energy, and begin to explore some of the many applications of electricity.

In the previous modules, we discussed electric charge and the force between charges. We also talked about something probably new to most of you – the electric field, which is produced by electric charge. I mentioned how the electric field stores energy and that energy can be used to exert a force on a charge: . Now we will delve deeper into the energy stored in an electric field. We will use gravity and gravitational potential energy as an analog to electric potential energy because there are many similarities between them. And we will introduce something that may seem new to you – electric potential – but is actually quite common. You’ve all used a battery before, right? And a battery has a voltage, like 9 V or 1.5 V in most household batteries. Well, voltage is an electric potential difference. So, the topic of this module is not actually new to you, instead it is just explained with new terminology.

#### 3.1 Electric Potential Energy

• Define the work done by an electric force
• Define electric potential energy
• Apply work and potential energy in systems with electric charges

#### 3.2 Electric Potential and Potential Difference

• Define electric potential, voltage, and potential difference
• Define the electron-volt
• Calculate electric potential and potential difference from potential energy and electric field
• Describe systems in which the electron-volt is a useful unit
• Apply conservation of energy to electric systems

#### 3.3 Calculations of Electric Potential

• Calculate the potential due to a point charge
• Calculate the potential of a system of multiple point charges
• Describe an electric dipole
• Define dipole moment
• Calculate the potential of a continuous charge distribution

#### 3.4 Determining Field from Potential

• Explain how to calculate the electric field in a system from the given potential
• Calculate the electric field in a given direction from a given potential
• Calculate the electric field throughout space from a given potential

#### 3.5 Equipotential Surfaces and Conductors

• Define equipotential surfaces and equipotential lines
• Explain the relationship between equipotential lines and electric field lines
• Map equipotential lines for one or two point charges
• Describe the potential of a conductor
• Compare and contrast equipotential lines and elevation lines on topographic maps